186 ELECTRIC UNITS OF CHARGE BY G. C. LAURENCE. B. SC. 



ebonite screws (s) that supported them until the galvanometer 

 reading was moved as far to the right as it would go. By this 

 method the cylinders could be adjusted much more easily and 

 more accurately than by mechanical methods. This was shown 

 by the fact that a capacity .14 m. m. f. (i. e. .12% of the total 

 capacity, 123.50 m. m. f.) smaller was obtained with this 

 method of adjusting, than was obtained with a mechanical 

 method. The mechanical method consisted in adjusting the 

 width of the space between the inner and outer cylinders at 

 different places around the circumference by inserting a wedge 

 therein. 



Measuring the Effect of a Slight Bend in one of the 

 Cylinders on their Capacity 



The relative increase in the capacity of a cylindrical con- 

 denser caused by a small displacement x of the axis of the inner 

 cylinder parallel to itself is ^C/C = x\/4:R{R-r)* , provided that 

 X is small compared with R-r, the difference in radius of the 

 cylinders. Hence the capacity of an element of length dy is 



dC=(x'/4R[R-r)-^\) dy /2 log {R-r) (1) 



It was found that the inner cylinder was slightly curved, de- 

 viating at the most about .05mm. from a straight line. Con- 

 sidering this curve to be parabolic, taking the axis of the outer 

 cylinder as the Y axis, and the origin at the middle of the cylinder 

 we get in the case of the electrically adjusted cylinders x — 

 {y^-h)/M, where M is the latus rectum and A is a constant of 

 such a size as will make the total capacity a minimum. Inte- 

 grating for the whole length of the cylinder (frovi -L/2 to -\-L/2) 

 we get for the capacity 



C = (L^/S0—hD/6—h-L) I {SM'R{R-r) log (i?/r))+C (2) 



where C is the capacity the cylinders would have if their axes 



* loc. cit,, page 484 



